Abstract
We study in this paper the radiative corrections to chiral magnetic current at both zero and nonzero temperature. Our motivation is a radiative correction to the matrix element of the anomalous Ward identity in massless QED stemming from a three-loop diagram where the two photons coming from the one-loop anomalous triangle are re-scattered. Through the interplay between the Ward identity and the infrared subtlety of the fermion loop integral, we are able to reproduce the corrections known in literature in a simpler approach and obtain its contribution to the chiral magnetic current at zero temperature. At a nonzero temperature, the infrared subtlety disappeared in a static magnetic field and the three-loop diagram does not contribute to the chiral magnetic current any more. The generalization to all orders of the massless QED and the QCD corrections are discussed.
Highlights
Anomaly-induced transport phenomena in systems with chiral fermions have attracted wide interests ranging from high-energy physics to condensed matter physics [1]
Our statement on the absence of the radiative correction is limited to the three-loop diagram Fig. 1 with the two internal photon lines replaced by two gluon lines, and this is of the order Oðg4Þ in Yang-Mills coupling
Through the interplay between the vector Ward identity and the infrared singularity with massless fermions, we are able to rederive, in a much simpler way, the known corrections from the three-loop diagram in Fig. 1 at zero temperature. This type of radiative correction does not invalidate the Adler-Bardeen theorem since the kinematic point required by the theorem cannot be reached for a massless fermion field, but it does contribute to the chiral magnetic current in the massless limit at zero temperature
Summary
Anomaly-induced transport phenomena in systems with chiral fermions have attracted wide interests ranging from high-energy physics to condensed matter physics [1]. Twenty years after the discovery of the nonrenormalization theorem of chiral anomalies, the authors of [19] found a radiative correction to (3) for massless QED, which is UV divergent This correction is contributed by the three-loop diagram, where the two photons from the upper triangle are rescattered and the anomalous Ward identity is modified to the form ðQ1 þ Q2ÞρΛμνρðQ1; Q2Þ 1⁄4 −×i2e1π22−ε6μ3ν4αeπβ44Ql1oαgQΛk22β2; ð6Þ with Λ the ultraviolet cutoff and k the infrared cutoff depending on Q1 and Q2. After taking the limit (8) or (9) of the top triangle, the real time formulation can be converted into Matsubara formulation for a static magnetic field, where the infrared behavior is transparent, and the same form of the limits (8) or (9) for the summation of the one-loop and three-loop diagrams emerges In another word, the term on the rhs of (8) that is linear in q is not subject to the radiative corrections of Fig. 1 and the classical formula (5) is intact.
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